Section A
Multiple Choice Questions — 15 Questions
(+4 / -1)
1
arithmetic
easy
Evaluate: (5 × 7 × 2 × 17) ÷ (14 × 34 × 35)
The source PDF prints no A/B/C/D/E letters for these options; labels here follow the exact on-page top-to-bottom order.
A
14
B
0.71
C
0.071
D
17
E
1/17
Show answer
Answer: C
The denominator can be rewritten as 14 × 34 × 35 = (2 × 7) × (2 × 17) × (5 × 7). The numerator is 5 × 7 × 2 × 17. Cancelling the common factors 5, 7, 2 and 17 once each from numerator and denominator leaves 1 ÷ (2 × 7) = 1/14 = 0.071 (rounded to three decimal places).
2
number-theory
easy
What is the value of 0¹?
A
0
B
1
C
∞
D
10
E
None of the above
Show answer
Answer: A
Zero raised to anything remains zero.
3
geometry
medium
A triangle has sides 35 cm, 37 cm and 12 cm. Identify the type of the triangle..
A
Acute angle triangle
B
Obtuse triangle
C
Right-angled triangle
D
It cannot be determined from knowing just the side lengths
E
Open triangle
Show answer
Answer: C
These numbers are a Pythagorean triplet (12² + 35² = 144 + 1225 = 1369 = 37²); and therefore, this represents a right-angled triangle.
4
patterns
medium
A child gets $10 pocket money every day. He saves $1 on the first day, $2 on the second day, $3 on the third day, $4 on the fourth day, and so on. On which day will he have saved enough to buy his sister a $50 school bag?
A
Day 50
B
Day 25
C
Day 9
D
Day 10
E
Day 5
Show answer
Answer: D
Make a table of cumulative savings: Day1=1, Day2=1+2=3, Day3=3+3=6, Day4=6+4=10, Day5=10+5=15, Day6=15+6=21, Day7=21+7=28, Day8=28+8=36, Day9=36+9=45, Day10=45+10=55. As shown, he has enough money to buy the $50 bag on Day 10.
5
ratio-proportion
easy
A photographer expands a photo diagonally in a software, to make it fit into a digital album. The bigger photo is neither squished nor stretched and looks proper. The original dimensions of the photo were 6 inches by 4 inches. Now the stretched photo is of the dimensions 12 inches by p inches. Find the value of p.
A
8 inches
B
12 inches
C
10 inches
D
2 inches
E
None of the above
Show answer
Answer: A
This is the right way to stretch any rectangular box so that its proportions remain the same, i.e., it does not get squished or stretched disproportionately. Keeping the same proportion means if the height is stretched to n times its original, the width should also be stretched to n times its original. For the original image, height = 6 inches, width = 4 inches. For the new image, the height is increased to twice its original: new height = 6×2 = 12 inches; therefore, new width = 4×2 = 8 inches. (Note that stretching and crunching involve multiplication or division, not addition or subtraction.)
6
geometry
easy
How many lines of symmetry does a parallelogram have?
A
1
B
2
C
3
D
0
Show answer
Answer: D
A parallelogram does not have any line of symmetry. Take a paper, cut out a parallelogram, and see if there is any way you can fold it such that there is no spillover — there isn't.
7
arithmetic
easy
Evaluate: 32.345 + 32.435 − 23.435
A
88.215
B
-23.435
C
41.345
D
-23.525
E
23.345
Show answer
Answer: C
32.345 + 32.435 − 23.435 = 41.345.
8
fractions
medium
Assume that all sections within each of the given shapes are the same size. Consider only the area represented by the flower, the circle, etc. without including any surrounding area around it. Which figure has the smallest fraction of itself shaded?
The image itself labels each shape with a lowercase letter (a–e); the option labels below use the paper's uppercase A–E convention in that same left-to-right order, and each option's text preserves the original 'Shape a', 'Shape b', … wording.
A
Shape a
B
Shape b
C
Shape c
D
Shape d
E
Shape e
Show answer
Answer: C
Shape a has shaded part = 8/12 = 4/6 = 2/3 = 0.66. Shape b has 2/5 shaded = 0.4. Shape c has 1/3 shaded = 0.33. Shape d has 6/11 shaded = 0.545. Shape e has 7/9 shaded = 0.778. 1/3 is the smallest fraction here. Therefore, the correct choice is shape C.
9
combinatorics
medium
The number of shortest paths along a 3 × 3 grid from one corner to the diagonally opposite corner is:
A
1
B
2
C
3
D
6
E
12
Show answer
Answer: D
Count the number of ways from the top-left corner to the bottom-right corner by adding, at each intersection, the number of ways to reach the intersection above it and the intersection to its left (starting from 1 way along the top row and left column). This builds up to 1, 1, 1 in the first row/column, then 1, 2, 3 in the next, then 1, 3, 6 in the last — giving 6 ways to reach the diagonally opposite corner.
10
rate-problems
easy
Look at the following table: Which two cars are going at the same speed?
Car A: Distance Travelled 40 km, Time taken 1 hour
Car B: Distance Travelled 30 km, Time taken 2 hours
Car C: Distance Travelled 40 km, Time taken 2 hours
Car D: Distance Travelled 20 km, Time taken 30 minutes
A
A & B
B
B & C
C
A & C
D
A & D
E
All are going at different speeds
Show answer
Answer: D
Speed = Distance/time [Be careful to use the same units for time to compare!]. Speed of A = 40/1 = 40 km/h, Speed of B = 30/2 = 15 km/h. Speed of C = 40/2 = 20 km/h. Speed of D = 20 ÷ (1/2) = 40 km/h [Converting 30 minutes to half an hour]. Cars A and D both travel at 40 km/h, so A & D are going at the same speed.
11
spatial-reasoning
medium
A paper is folded as shown below and punched in its folded state. When the paper is opened out again, what will be the pattern of holes formed?
The source PDF prints no letters for these options; labels here follow the exact on-page top-to-bottom order. Each option below is itself an image; the correct option was determined by visually matching the small confirmation image printed in the paper's own Answers section against these four option images.
Show answer
Answer: D
The source's own explanation for this question is to physically test it: 'Cut out a piece of paper and try it out.' Folding the triangle along the marked lines and punching a hole through all layers in the folded state reproduces, once the paper is unfolded, the hole pattern shown in option D — two punches close together near the left side of the triangle and one punch at the bottom-right corner — which matches the paper's own printed confirmation image for this question.
12
sets
medium
A sports club offers three sports – soccer, basketball and baseball. All their members play at least one sport. Which of the following Venn diagrams represents the members of the sports club? Assume that there are no limits to the number of sports one can play and that some people may be physically strong enough and able enough to play any or all sports.
The source PDF prints no letters for these options; labels here follow the exact on-page top-to-bottom order. Each option below is itself an image.
Show answer
Answer: A
Some members play: only soccer, only basketball, or only baseball. Some members play 2 sports. Some members play all 3 sports. Since all members play at least one sport, there are no members playing none of the sports. Hence the choice is A — three separate, pairwise-overlapping circles with no 'outside all circles' region.
13
geometry
medium
A rectangular park is to be fenced with a stone wall. There is a gate along the perimeter that is 2 m long, which is made of steel. Find the cost of fencing the park, if its dimensions are 100 m by 50 m. The entire perimeter may be taken to be the same height of 3 m. Take the cost of stone fencing at $23 per m² and steel fencing at $17 per m².
A
$10,384
B
$6,900
C
$20,700
D
$456
E
$20,785
Show answer
Answer: E
Here the cost of fencing is given per square meter. That means you need to consider the surface area of the perimeter material used. Area of steel required = 2 × 3. Cost of steel material = 2 × 3 × 17 = $85. Area of stone required = 2(100 + 50) × 3. Cost of stone material = 900 × 23 = $20700. Total cost = $20,785.
14
number-theory
easy
How many three-digit natural numbers are divisible by 5? Natural numbers are positive integers starting from 1.
A
200
B
201
C
180
D
198
E
199
Show answer
Answer: C
You could use the AP formula aₙ = a + (n−1)d. The nth term is the last number before 1000 that is divisible by 5: aₙ = 995. a = 100, d = 5. Substituting, 995 = 100 + (n−1)5, so n = 179 + 1 = 180. Alternatively, counting multiples of 5 by range: 000–100: 1, 101–200: 20, 201–300: 20, 301–900: 120, 901–999: 19, giving a total of 180.
15
arithmetic
medium
The interest on $1200 is more than the interest on $1000 by $30 in 3 years. Find the rate of interest for each year.
A
6%
B
5.5%
C
4%
D
Cannot be found
Show answer
Answer: 5%
Assuming a simple interest of r% per annum, 3-year interest on $1000 = 30r. 3-year interest on $1200 = 36r. Difference = 6r = $30. Hence R = 5% p.a.
Section B
Open-Ended (Integer) Questions — 10 Questions
(+5)
16
arithmetic
easy
Evaluate: (45 × 37 × 27) ÷ 185
Show answer
Answer: 243
185 = 5 × 37, so (45 × 37 × 27) ÷ 185 = (45 × 27 × 37) ÷ (5 × 37). The factor of 37 cancels completely, and 45 ÷ 5 = 9, leaving 9 × 27 = 243.
17
data-interpretation
medium
Several people were surveyed for their preference for 4 drinks A, B, C and D. All the people surveyed are represented in the graph below. If the fraction of people who preferred A to those who preferred D is m/n, what is m + n?
Show answer
Answer: 8
From the bar graph, the number of people who preferred A is 150, and the number who preferred D is 250. The fraction of people who preferred A to those who preferred D is 150/250 = 15/25 = 3/5. So, m + n = 3 + 5 = 8.
18
number-theory
easy
Find the smallest integer, which when divided by 7 gives a remainder of 0, but when divided by 10 gives a remainder of 1
Show answer
Answer: 21
The smallest number that is just 1 over a multiple of 10, which is also a multiple of 7, is 21.
19
3d-geometry
hard
A steel cuboid is reshaped into a cube. Initially, its length, breadth, and depth were 270 cm, 100 cm, and 64 cm respectively. Find the sum of digits of the surface area of the cube.
Show answer
Answer: 18
The volume remains the same, since the amount of material used stays the same. Volume of cuboid = 270×100×64 = 1,728,000 cm³. Since the new shape is a cube, each side is the cube root of 1,728,000. This number ends with three zeroes, so each side ends with one zero (ones place is 0). Looking at 1728: it ends in 8, so each side has a tens place of 2; and 1728 is the cube of a two-digit number between 10 and 20, which must be 12 (12³ = 1728). Therefore, each side of the cube (in cm) is 120. Total surface area of the cube = 6 × side × side = 6 × 120 × 120 = 86,400 cm². Sum of digits = 8 + 6 + 4 + 0 + 0 = 18.
20
geometry
medium
Two identical rectangular cards partially overlap. The area of overlap is a square with an area 4 cm², and the total area of the regions of the faces of the two cards that do not overlap is 12 cm². What is the area of one card?
Show answer
Answer: 10
The area of both rectangles together = sum of the non-overlapping regions + the area of the overlap square counted twice (once for each rectangle) = 12 + 4 + 4 = 20 cm². Therefore, the area of each rectangle is half of the area of both rectangles together = 20/2 = 10.
21
patterns
medium
Find the sum of digits of the next number in the series: 11, 143, 2431, 46189, ____
Show answer
Answer: 23
The prime numbers after 10 are 11, 13, 17, 19, 23, .... The series is formed by multiplying them consecutively: 11, 11×13, 11×13×17, 11×13×17×19, .... The next one is therefore 11×13×17×19×23 = 1,062,347. Sum of digits = 1+0+6+2+3+4+7 = 23.
22
statistics
easy
The mean of four consecutive odd numbers is 24. Find the sum of the middle two numbers in this set.
Show answer
Answer: 48
Let the four consecutive odd numbers be n, n+2, n+4 and n+6. Their mean is (n + (n+2) + (n+4) + (n+6)) / 4 = (4n + 12) / 4 = n + 3. Since the mean is 24, n + 3 = 24, so n = 21. The four numbers are 21, 23, 25 and 27, and the middle two are 23 and 25. Their sum is 23 + 25 = 48.
23
number-theory
medium
Find the largest four-digit number which when divided by 4, 7, and 13 leaves a remainder of 3 in each case.
Show answer
Answer: 9831
LCM(4,7,13) = 364. The largest 4-digit number is 9999. To be divisible by 364, note that 9999 ÷ 364 = 27 remainder 171 (9999 − 171 = 9828 is the largest multiple of 364 that is at most 9999). To account for the required remainder, we add it back: 9828 + 3 = 9831.
24
exponents
medium
2⁴⁰⁰ can be equivalently written as a repeated product of the number 16. For example, 16 × 16 × 16 × ... (n times). What is the value of n?
Show answer
Answer: 100
2⁴⁰⁰ is 2⁴ raised to 100. That is 16 raised to 100, that is, 16 multiplied by itself 100 times. Thus, n = 100.
25
patterns
medium
Theo's football coaching starts at 6:30 am, and his mother wants him to wake up at 6 am to be on time for coaching. But currently, Theo wakes up late. Theo promises to wake up 5 minutes earlier than he did the day before. If Theo woke up at 6:50 am on a Sunday, and keeps his promise every day, on what day will he wake up on time for football coaching? Leave your answer as 0001 for Monday, 0002 for Tuesday, ..., and 0007 for Sunday.
Show answer
Answer: 0003
Make a table: Sunday 6:50 am (day 0), Monday 6:45 am (day 1, 5 minutes earlier), Tuesday 6:40 am (day 2, 5 minutes earlier), and so on. We need Theo to wake up 50 minutes earlier than 6:50 am to reach 6:00 am. On day n (counting from Sunday), Theo wakes up 5n minutes earlier than he did on Sunday. Since 5n = 50 gives n = 10, on day 10 he wakes up on time. Counting 10 days on from Sunday (day 7 is the following Sunday, day 8 Monday, day 9 Tuesday, day 10 Wednesday), day 10 is a Wednesday. Wednesday is the 3rd day of the week under the paper's Monday=0001 convention, so the answer is 0003.